Question

What is the 95th term of the following letter series?
A, A, B, B, B, B, C, C, C, C, C, C, D, D, D, D, D, D, D, D, E, ...

• A. H
• B. I
• C. J
• D. K

Answer 1

The Correct Option is C

To find the 95th term of the given letter series, we first need to identify the pattern:

The series is: A, A, B, B, B, B, C, C, C, C, C, C, D, D, D, D, D, D, D, D, E, ...

Upon analyzing the pattern, we observe that:

• The letter 'A' appears 2 times.
• The letter 'B' appears 4 times.
• The letter 'C' appears 6 times.
• The letter 'D' appears 8 times.
• and so on...

The number of times each letter appears increases successively by 2. This suggests the pattern follows the formula:

n = 2k where k is the position of the group (A = 1, B = 2, C = 3, ...).

Next, we calculate the cumulative count of terms to determine where the 95th term falls:

• 1st group (A): 2 terms
• 2nd group (B): 4 terms (cumulative 6 terms)
• 3rd group (C): 6 terms (cumulative 12 terms)
• 4th group (D): 8 terms (cumulative 20 terms)
• 5th group (E): 10 terms (cumulative 30 terms)
• 6th group (F): 12 terms (cumulative 42 terms)
• 7th group (G): 14 terms (cumulative 56 terms)
• 8th group (H): 16 terms (cumulative 72 terms)
• 9th group (I): 18 terms (cumulative 90 terms)
• 10th group (J): 20 terms (cumulative 110 terms)

Therefore, the 95th term falls in the 10th group where the letter is 'J'. The cumulative count from the previous group (9th group) is 90, so the 95th, 96th, ..., 110th terms are all 'J'.

Consequently, the 95th term in this series is J.